Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = -xi-yj+z3k, S is the part of the cone z = x²+y2 between the planes z = 1 and z = 2 with downward orientation 15л ZA z=2

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A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: Find the flux of the vector field F = (y, z, x) across the part of the plane z = 3 + 4x + y above…

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Q: of the vector field F across the surface S in the indicated direction. F = x 2y i  - z k; S is…

A: Introduction: The flux of the vector field F is given by the formula, ∮CF.ndS=∫∫∫div(F)dA

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Q: 2. Let C be the curve of intersection between the cylinder r2+y = 1 and r-2y+z = 0, oriented…

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